Next time: sections 1.1 |
4x6 cards:
We will be covering portions of the following chapters (7th edition):
On Thursday, we'll dive into the problems in the highlight worksheet, as well as some of the homework problems.
Feel free to remind me to scan the homework problems: I know that some of you may not have the book. I haven't yet scanned these ones, but I'll try to tonight.
I ask that you keep the phones out of sight. It's really distracting for me to see someone playing on their phone during class. And if I get too distracted, I absent-mindedly begin thinking about making quizzes and tests harder...:)
We'll begin with some historical, perhaps hysterical, logic: that of Lewis Carroll's unusual "logic game". Contemporaneous with John Venn, he created his own system for solving logic problems.
Besides the nine Counters, it also requires one Player, AT LEAST. I am not aware of any Game that can be played with LESS than this number: while there are several that require MORE: take Cricket, for instance, which requires twenty-two. How much easier it is, when you want to play a Game, to find ONE Player than twenty-two. At the same time, though one Player is enough, a good deal more amusement may be got by two working at it together, and correcting each other's mistakes.
An example syllogism:
What is the logical conclusion, assuming that the premises are true? Let's ask chatGPT.
The method: eliminating the common term
So, in the baby example, the common term "crazy" is eliminated, and we arrive at the obvious conclusion:
I'm going to give you a Logic Game handout now, so that you can "play along" (perhaps with another person, so that "...a good deal more amusement may be got by two working at it together, and correcting each other's mistakes. How would Carroll have suggested we arrive at this conclusion?
If I were Lewis Carroll, I'd also give you a board, and nine counters: five grey, and four red. Here's a picture of his board, and his description of the meaning of the counters:
(By the way, in Section 1.2 we'll turn these into implications, and use a technique known as "hypothetical syllogism" to reach that conclusion.)
Conclusion: Aristotle is mortal.
Let's arrive at this conclusion by the Logic Game.
(We'll characterize these modifiers -- some, none, all -- as "quantifiers": they tell "how many"; and these "propositions" will be characterized as "predicates" in Section 1.3).
Some statements come with "implied quantifiers" (real speech can be very irritating that way!): for example, in the example above, "Babies are crazy" should be interpreted to mean "All babies are crazy." There's an implied universal ("all") quantifier.
Other statements need to be re-written to look like our three types of propositions: e.g. "None but the brave deserve the fair" is re-written as "No not-brave persons are persons that deserve the fair."
The story reminds me of a poem by A. E. Housman: The Laws of God, The Laws of Man. The reason that the story of Protagoras and Eualthus is a dilemma, a paradox, or a quandary, is that there are two different systems of laws operating.